Universal obstructions for embedding extension problems

Australasian Journal of Combinatorics

Volumn 36, Issue , 2006, Pages 39-68

  Mohar, Bojan ^a,b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 57949115689     PISSN: 10344942     EISSN: 22023518     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. D. Archdeacon, The complexity of the graph embedding problem, in Topics in Combinatorics and Graph Theory, R. Bodendiek and R. Henn (eds.), Physica- Verlag, Heidelberg, 1990, pp. 59-64.
2. D. Archdeacon and P. Huneke, A Kuratowski theorem for nonorientable surfaces, J. Combin. Theory Ser, B 46 (1989), 173-231.
3. K. S. Booth and G. S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-trees, J. Comput. System Sci. 13 (1976), 335-379.
4. N. Chiba, T. Nishizeki, S. Abe and T. Ozawa, A linear algorithm for embedding planar graphs using PQ-trees, J. Comput. System Sci. 30 (1985), 54-76.
5. S. A. Cook and R. A. Reckhow, Time bounded random access machines, J. Comput. Syst. Sci. 7 (1976), 354-375.
6. H. Djidjev and J. H. Reif, An efficient algorithm for the genus problem with explicit construction of forbidden subgraphs, 23rd Annual ACM Symposium on Theory of Computing, New Orleans, LA, May 1991, pp. 337-347.
7. o(g)) steps, in Proc. 11th Ann. ACM STOC, Atlanta, Georgia (1979) pp. 27-37.
8. H. de Fraysseix and P. Rosenstiehl, A depth-first search characterization of planarity, Ann. Discr. Math. 13 (1982), 75-80.
9. J. L. Gross and T. W. Tucker, Topological graph theory, Wiley-Interscience, New York, 1987.
10. J. E. Hopcroft and R. E. Tar j an, Dividing a graph into triconnected components, SIAM J. Comput. 2 (1973), 135-158.
11. J. E. Hopcroft and R. E. Tarjan, Efficient planarity testing, J. ACM 21 (1974), 549-568.
12. M. Juvan, J. Marincek and B. Mohar, Elimination of local bridges, Math. Slo- vaca 47 (1997), 85-92.
13. M. Juvan, J. Marincek and B. Mohar, Embedding graphs in the torus in linear time, in Integer programming and combinatorial optimization, E. Balas and J. Clausen (Eds.), Lect. Notes in Computer Science 920, Springer, Berlin, 1995, pp. 360-363.
14. M. Juvan and B. Mohar, Obstructions for 2-Mobius band embedding extension problem, SIAM J. Discrete Math. 10 (1997), 57-72.
15. M. Juvan and B. Mohar, 2-restricted extensions of partial embeddings of graphs, Europ. J. Combin. 26 (2005), 339-375.
16. B. Mohar, Projective planarity in linear time, J. Algorithms 15 (1993), 482-502.
17. B. Mohar, Obstructions for the disk and the cylinder embedding extension problems, Combin, Probab. Comput. 3 (1994), 375-406.
18. B. Mohar, Projective plane and Mobius band obstructions, Combinatorica 17 (1997), 235-266.
19. B. Mohar, A linear time algorithm for embedding graphs in an arbitrary surface, SIAM J. Discrete Math. 12 (1999), 6-26.
20. N. Robertson and P. D. Seymour, Graph minors. VIII. A Kuratowski theorem for general surfaces, J. Combin. Theory, Ser. B 48 (1990), 255-288.
21. N. Robertson and P. D. Seymour, Graph minors XIII. The disjoint paths problems. J. Combin. Theory Ser. B 63 (1995), 65-110.
22. N. Robertson and P. D. Seymour, An outline of a disjoint paths algorithm, in: Paths, Flows, and VLSI-Layout (B. Korte, L. Lovasz, H. J. Promel and A. Schrijver Eds.), Springer-Verlag, Berlin, 1990, pp. 267-292.
23. C. Thomassen, The graph genus problem is NP-complete, J. Algorithms 10 (1989), 568-576.
24. W. T. Tutte, How to draw a graph, Proc. London Math. Soc. 13 (1963), 743-768.
25. S. G. Williamson, Embedding graphs in the plane-algorithmic aspects, Ann. Discrete Math. 6 (1980), 349-384.
26. S.G. Williamson, Depth-first search and Kuratowski subgraphs, J. ACM 31 (1984), 681-693.